Diagonals of solutions of the Yang-Baxter equation

Abstract: The Yang--Baxter equation is one of the fundamental equations occurring in statistical mechanics and quantum field theory. I will show that the diagonal mappings are bijections in any non-degenerate set-theoretical solution. This immediately gives that any non-degenerate solution is bijective and affirmatively answers question stated by Cedo, Jespers and Verwimp. I also prove that, for a subclass of solutions called permutational, one-sided non-degeneracy is sufficent for the diagonal to be invertible. This is joint work with Premysl Jedlicka (Czech University of Life Sciences).

quantum algebrarings and algebras

Audience: researchers in the topic

European Non-Associative Algebra Seminar